920,064 research outputs found
Stability and Complexity of Minimising Probabilistic Automata
We consider the state-minimisation problem for weighted and probabilistic
automata. We provide a numerically stable polynomial-time minimisation
algorithm for weighted automata, with guaranteed bounds on the numerical error
when run with floating-point arithmetic. Our algorithm can also be used for
"lossy" minimisation with bounded error. We show an application in image
compression. In the second part of the paper we study the complexity of the
minimisation problem for probabilistic automata. We prove that the problem is
NP-hard and in PSPACE, improving a recent EXPTIME-result.Comment: This is the full version of an ICALP'14 pape
Revisiting the Complexity of Stability of Continuous and Hybrid Systems
We develop a framework to give upper bounds on the "practical" computational
complexity of stability problems for a wide range of nonlinear continuous and
hybrid systems. To do so, we describe stability properties of dynamical systems
using first-order formulas over the real numbers, and reduce stability problems
to the delta-decision problems of these formulas. The framework allows us to
obtain a precise characterization of the complexity of different notions of
stability for nonlinear continuous and hybrid systems. We prove that bounded
versions of the stability problems are generally decidable, and give upper
bounds on their complexity. The unbounded versions are generally undecidable,
for which we give upper bounds on their degrees of unsolvability
Complexity of Stability
Graph parameters such as the clique number, the chromatic number, and the independence number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to social networks. In particular, the chromatic number of a graph (i.e., the smallest number of colors needed to color all vertices such that no two adjacent vertices are of the same color) can be applied in solving practical tasks as diverse as pattern matching, scheduling jobs to machines, allocating registers in compiler optimization, and even solving Sudoku puzzles. Typically, however, the underlying graphs are subject to (often minor) changes. To make these applications of graph parameters robust, it is important to know which graphs are stable for them in the sense that adding or deleting single edges or vertices does not change them. We initiate the study of stability of graphs for such parameters in terms of their computational complexity. We show that, for various central graph parameters, the problem of determining whether or not a given graph is stable is complete for ???, a well-known complexity class in the second level of the polynomial hierarchy, which is also known as "parallel access to NP.
Complexity of Stability
Graph parameters such as the clique number, the chromatic number, and the
independence number are central in many areas, ranging from computer networks
to linguistics to computational neuroscience to social networks. In particular,
the chromatic number of a graph (i.e., the smallest number of colors needed to
color all vertices such that no two adjacent vertices are of the same color)
can be applied in solving practical tasks as diverse as pattern matching,
scheduling jobs to machines, allocating registers in compiler optimization, and
even solving Sudoku puzzles. Typically, however, the underlying graphs are
subject to (often minor) changes. To make these applications of graph
parameters robust, it is important to know which graphs are stable for them in
the sense that adding or deleting single edges or vertices does not change
them. We initiate the study of stability of graphs for such parameters in terms
of their computational complexity. We show that, for various central graph
parameters, the problem of determining whether or not a given graph is stable
is complete for \Theta_2^p, a well-known complexity class in the second level
of the polynomial hierarchy, which is also known as "parallel access to NP.
The architecture of predator-prey and the relationship between complexity and stability
Theoretical studies predict that the stability of an ecosystem is negatively correlated with its complexity, measured by the number of interacting species. On the other hand, empirical evidence indicates that food webs are highly interconnected. In this manuscript we present results on the stability two-level predator-prey food webs. We analyzed exhaustively all possible topologies of connections among species. Our findings show that those food webs fall into two classes with clearly distinct stability properties. In one of them stability is negatively correlated with complexity, and in the other group stability is positively correlated. For a positive relationship our results reveals highly structured food webs. The positive or negative relationship is related only to the topological structure of the food web. It is independent of the number of connections, strengths of predator-prey interactions or number of species. We review empirical evidence that corroborates our results
Electronic circuit delivers pulse of high interval stability
Circuit generates a pulse of high interval stability with a complexity level considerably below systems of comparable stability. This circuit is being used as a linear frequency discriminator in the signal conditioner of the Apollo command module
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